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Leila, Alan, and Miguel have a total of $102 in their wallets. Miguel has 2 times what Alan has. Leila has $10 more than Alan. How much does each have?

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Answer:

Alan has $23

Leila has $33

Miguel has $46

Explanation:

Let the variables L, A, and M represent the amounts Leila, Alan, and Miguel have.

Step 1: Create an expression to represent Miguel's amount:

Since Miguel has 2 times Alan's amount, we can represent this with the following expression:

M = 2A

Step 2: Create an expression to represent Leila's amount:

Since Leila has $10 more than Alan, we can represent with the following expression:

L = A + 10

Step 3: Set the sum of the expressions and A equal to $102:

We know that L + A + M = 102. Thus, we can plug in 2A for M and A + 10 for L to find A, Alan's amount:

2A + A + A + 10 = 102

4A + 10 = 102

4A = 92

A = 23

Thus, Alan has $23.

Step 4: Find Miguel's amount by plugging in 23 for A in M = 2A:

M = 2(23)

M = 46

Thus, Miguel has $46.

Step 5: Find Leila's amount by plugging in 23 for A in L + A + 10:

L = 23 + 10

L = 33

Thus, Leila has $33.

Step 6: Check that the sum of Leila, Alan, and Miguel's amounts is 102:

We can check that our answers are correct by making sure that the sum of Leila, Alan, and Miguel's amounts (33, 23, and 46 respectively) equals 102:

33 + 23 + 42 = 102

56 + 46 = 102

102 = 102

Thus, our answers are correct.

User Jan Herrmann
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